MA 15910 Midterm: Exam 2 Fall 2014 Solutions

Problem #2: Consider the following matrix A=10 4 0 Find a matrix P which diagonalizes A -호 1 02 (C)10 D0 01 (E)0 1-2 0-5 1 (F)10 (G)0 1(H)0 0(I) 01 0 0 01 Problem #2: Select Just Save Submit Problem #2 for Grading Attempt #2 | Attempt #3 Problem #2 | Attempt #1 Your Answer Your Mark:

Math 227 Exam 4- Page 7 of 8 Due: 12/01/2017 6. Evaluate ll. F . ids with F = (z-12 , 2zy , 2) and S: boundary of region enclosed on top by the plane z = 4 and below by the parabaloid z = z2+ Math 227 Exam 4-Page 8 of 8 Due: 12/01/2017 Bonus (no partial credit): It turns out that F-(-y , x , zy-vray satisfies ▽ × F*-x2 , 2ry , 2). (the field from problem 6) Use this fact, Stokes' Theorem, and properties of surface/line integrals to answer problem 6 without doing any computations.

1. Evaluate (3x-2-7x6 + 2) dr 2 mar b. 2. Evaluate ma 2 3. Assume that f,f(x)dr=10 jf(x)dx=15 and 12 ma Find 3s(x)dr a. 75 b. 15 C.-15 d. 75 4. Evaluate [(tan(2x)) sec2 (2r)dx 12 ma b. (tan 2x)' +c d. 8(tan 2x)+e a. tan 2x)+